Abstract
The rank-3 antisymmetric tensors which are the magnetic monopoles of SU(N) Yang–Mills gauge theory dynamics, unlike their counterparts in Maxwell’s U(1) electrodynamics, are non-vanishing, and do permit a net flux of Yang–Mills analogs to the magnetic field through closed spatial surfaces. When electric source currents of the same Yang–Mills dynamics are inverted and their fermions inserted into these Yang–Mills monopoles to create a system, this system in its unperturbed state contains exactly three fermions due to the monopole rank-3 and its three additive field strength gradient terms in covariant form. So to ensure that every fermion in this system occupies an exclusive quantum state, the Exclusion Principle is used to place each of the three fermions into the fundamental representation of the simple gauge group with an SU(3) symmetry. After the symmetry of the monopole is broken to make this system indivisible, the gauge bosons inside the monopole become massless, the SU(3) color symmetry of the fermions becomes exact, and a propagator is established for each fermion. The monopoles then have the same antisymmetric color singlet wavefunction as a baryon, and the field quanta of the magnetic fields fluxing through the monopole surface have the same symmetric color singlet wavefunction as a meson. Consequently, we are able to identify these fermions with colored quarks, the gauge bosons with gluons, the magnetic monopoles with baryons, and the fluxing entities with mesons, while establishing that the quarks and gluons remain confined and identifying the symmetry breaking with hadronization. Analytic tools developed along the way are then used to fill the Yang–Mills mass gap.
Highlights
After the discovery of the muon in 1936, Rabi is said to have exclaimed: “who ordered that?” But to this day, the same question can still be asked of the proton and neutron which are at the nuclear heart of the observed material universe, and of the other baryons
Treating the monopole as a “system” to which the Exclusion Principle must be applied, and so using SU(3) to enforce an exclusive quantum state for each of these three fermions, and following a form of spontaneous symmetry breaking which moves a degree of freedom from gauge bosons to fermions, makes the bosons massless and renders SU(3) an exact symmetry, these YM magnetic monopoles acquire the same SU(3) antisymmetric color singlet wavefunction as baryons, and the magnetic field analogs which flow through the monopole surfaces obtain the same symmetric color singlet wavefunction as mesons. This enables the three fermion states inside the monopole to be identified as confined colored quarks, the gauge bosons to be identified as confined colored gluons, the YM magnetic monopoles to be identified as baryons, the mesons to be identified as quanta of the YM magnetic fields which net flow in and out of these monopoles, and the symmetry breaking to be identified with ultra-high-energy hadronization from a plasma of free quarks and gluons
SU(3) Quantum Chromodynamics (QCD) itself becomes no longer just a highly successful postulate both theoretically and experimentally; rather it comes to rest, fully intact, on a deeper dynamic foundation: Because the ground state “signal” monopole is a system containing precisely three fermions, the Exclusion Principle naturally places these fermions into the fundamental representation of SU(3), which becomes exact once symmetry is broken and hadronization of the plasma is complete
Summary
After the discovery of the muon in 1936, Rabi is said to have exclaimed: “who ordered that?” But to this day, the same question can still be asked of the proton and neutron which are at the nuclear heart of the observed material universe, and of the other baryons. This enables the three fermion states inside the monopole to be identified as confined colored quarks, the gauge bosons to be identified as confined colored gluons, the YM magnetic monopoles to be identified as baryons, the mesons to be identified as quanta of the YM magnetic fields which net flow in and out of these monopoles, and the symmetry breaking to be identified with ultra-high-energy hadronization from a plasma of free quarks and gluons From this we answer Rabi’s question: baryons were ordered by Maxwell, Yang and Mills, with an assist from Weyl via gauge theory itself, from Fermi–Dirac–Pauli via Dirac’s quantum theory of the electron and the Exclusion Principle, from Gauss’s law for fluxes of magnetic fields through closed surfaces, from Einstein’s generally covariant formulation of magnetic monopoles as third-rank antisymmetric tensors, and with credit to Hamilton for pioneering non-commuting quaternions which later became the foundation of YM gauge theory in the form of Pauli matrices and their extension to SU(N). We employ the foregoing development to fill the Yang–Mills Mass Gap [2]
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